If the vectors $2\hat{i} + 2\hat{j} - 2\hat{k}$,$5\hat{i} + y\hat{j} + \hat{k}$,and $-\hat{i} + 2\hat{j} + 2\hat{k}$ are coplanar,then the value of $y$ is:

If $\theta$ is the angle between vectors $\vec{A}$ and $\vec{B}$,then what is the value of the product $(\vec{B} \times \vec{A}) \cdot \vec{A}$?

Find the angle between force $F = (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$ units and displacement $d = (5 \hat{i} + 4 \hat{j} + 3 \hat{k})$ units. Also,find the projection of $F$ on $d$.

Find the angle between two vectors $\vec A = 2\hat i + \hat j - \hat k$ and $\vec B = \hat i - \hat k$ in degrees.

$A$ vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards north. The vector product $\vec{A} \times \vec{B}$ is

If the component of the vector $\vec{A}$ along the vector $\vec{B}$ is twice the component of $\vec{B}$ along $\vec{A}$, then the ratio of magnitudes of vectors $\vec{A}$ and $\vec{B}$ is